電動機控制的理論基礎pemclab.cn.nctu.edu.tw/W3news/技術專欄/2007-05-17...2007/05/17...

台灣新竹‧交通大學‧前瞻電力電子中心 808實驗室 (電力電子系統與晶片設計實驗室)

國立交通大學電機與控制工程研究所

編輯：鄒應嶼教授

Advanced Power Electronics Center, NCTU, Taiwan

2007年5月17日

電動機原理與驅動技術【專題導讀】

電動機控制的理論基礎

台灣新竹交通大學前瞻電力電子中心808實驗室 (Power Electronics Systems and Chips Design Lab)電力電子系統與晶片、開關電源、綠色能源、數位電源、馬達驅動、伺服控制

Integration of Power, Motor, and Motion Control

Motor

III

III IVtorque

speed

Power Converter

amperes

volts

RBSOA/FBSOA

Four-QuadrantVoltage/AmpereControl

Four-QuadrantTorque/SpeedControl

Closed-LoopSpeed/PositionControl

DSP-BasedDigital Controller Mechanical Load

X

Y

CoordinatedMotion ProfileControl

feed drivespindle driveelectrical carelectrical railway.. .. ..

mP/DSP-Based Programmable Motion & Motor Control Techniques

New Solutions of Motion Control Problems Using Advanced Technology!

1

課程講義：【電動機原理與驅動技術】01：電動機控制的理論基礎交通大學 808-電力電子實驗室 May 2007

台灣新竹‧交通大學‧電機與控制工程研究所‧808實驗室電力電子系統晶片、數位電源、DSP控制、馬達與伺服控制

http://pemclab.cn.nctu.edu.tw/Lab-808: Power Electronics Systems & Chips Lab., NCTU, Taiwan

1/180

【電動機原理與驅動技術】

電動機控制的理論基礎

Filename: \Filename: \C01 投影片：電動機控制\【電動機原理與驅動技術】01：電動機控制的理論基礎.ppt

2007年5月17日

鄒應嶼教授

國立交通大學電機與控制工程研究所

LAB808NCTU

Lab808: 電力電子系統與晶片實驗室Power Electronics Systems & Chips, NCTU, TAIWAN

台灣新竹•交通大學•電機與控制工程研究所


http://powerlab.cn.nctu.edu.tw/Lab-808: Power Electronics Systems & Chips Lab., NCTU, Taiwan

2/180

【義隆電子】電動機原理與驅動技術：課程大綱

1. 電動機控制的理論基礎

2. 直流電機的原理、特性、與驅動控制

3. 交流感應電機的原理與特性

4. 交流同步電機的原理與特性

5. 交流驅動系統簡介

6. 變頻器原理與交流脈寬調變技術

7. dq模型與向量控制技術

8. 交流伺服控制技術

9. 無刷直流馬達的無感測驅動控制

10. 交流感應馬達的無感測驅動控制

3/180

Motors for Modern Life

電力電子系統與晶片設計實驗室

Power Electronics Systems & Chips Lab.交通大學 • 電機與控制工程研究所

Power Electronics Systems & Chips Lab., NCTU, Taiwan

4/180

Motor Applications in Modern Life

Information TechnologyHouseholdsIndustry & ManufactureAutomobilesMedicineTransport etc. etc.

Motor55%

Other20%

Lighting21%

Computers4%

Electrical Energy 2002

Motors consume major electric energy!

5/180

Motors in a Household

How many motors are typically used in a household???virtually countless!!! They are found in:

refrigeratorcoffee mill dishwasher, washing machine food processor vacuum cleaner ventilator gardening machines video recorder CD player computer etc. etc.

6/180

Motor Applications in Modern Life

Insight, HONDA, 2000

2




7/180

Emerging Motor Drive Opportunities

Integrated Motor-Controller

IPEM

Currents

Control

++

ω & θ i

Est LPF

HFP

μ - Processor

IPEM

Con

trol

SYSTEM DESIGNPOWER ELECTRONICSCONTROL FIRM/SOFTWAREDIGITAL IC DESIGNANALOG IC DESIGN

POWER IC DESIGN

8/180

DVD-RW is the Core for Media Storage

DVD-RW

9/180

Motor Drives for Computers

Fan Motor for Switching Power Supply

Fan Motor for CPU Cooling

Spindle Motor for CD-ROMDC Motor for Open/Close

Voice Coil Motor for Optical Pickup Head

Spindle and Voice-Coil Motor for Hard Disk Drive

Motors for Floppy Disk Drive10/180

DVD系統方塊圖與主軸馬達控制與驅動IC

夾片機構

主軸馬達

光碟片光學

讀取頭長程尋軌馬達

數

位

信

號

處

理

器

DMA

記憶體

微控制器

IDE介面

碟片傳送馬達

控制電路

主軸伺服

聚焦伺服

循軌伺服尋軌伺服

滑動機構

DSP-Embedded Controller

Driver Circuit

DVD Servo Control IC

影音處理

驅動電路

Sensorless Spindle Motor Drive IC

主軸馬達驅動模組

11/180

DVD-Related Motor Driver ICs

Single-chip direct PWMSpindle motor driver +Actuator driver

LV8280TLV8200W

＊ LA6505＊ LA6506＊ LA6507

Spindle + actuator driver

Spindle motor drives providingPrecise rotation

LB11699HLB11698HLB1998LB1894M

LB11999HLB11996HLB11995HLB11975

Spindle Motor DriversUsing low-saturationVertical PNP transistors

LB1938TLB1930M

Spindle Motor Drivers

4chBTLLA6564HLA6553LA6544H/MLA6543MLA6542M

5chBTLLA6576LA6571

Actuator Drivers

High-output, high-gainActuator drives

12/180

無刷直流主軸馬達的結構

Outer Rotor Slot StatorHall effect sensors

3




13/180

Sensorless Control & Drive IC for Slim-Type DVD Spindle Motor

12

34

56

78

910

1112

1314

15 16 17 18 19 20 21 22 23 24 25 26 27 28

2930

3132

3334

3536

3738

3940

4142

4344454647484950515253545556

VO1F

VO1R

PGND1

VO2F

VO2R

PVCC1

PVCC1

VO3F

VO3R

P GND1

VO4F

VO4R

VO6F

VO6R

P GND3

P VCC3

VO5F

VO5R

SPRNF

W

P VCC2

V

P VCC2

U

SPRNF

Vref

CNF

6

CNF

5

CNF

4

CNF

1

CNF

3

CNF

2

IN2

IN3

IN1

IN4

IN5

IN6

INSP

FG

SW

RNF

FGHB

HU

P

HU

N

HV

P

HV

N

HW

P

HW

N

VC

C

GN

D

SPC

NF

GV

SW

MU

TE

SB

S TBY

Pre D

river

Fed

Lo

gic

Pre D

river

Fed

Lo

gic

Pre

Driv

er

Fed

Lo

gic

Pre

Driv

er

Fed

Lo

gic

ST

BY

SB

180

deg

MA

TR

IX

OC

C.

Lim

it

Pre

D

river

Pre

D

river

Pre

D

river

Pre D

river

Fed

Lo

gic

Pre D

river

Fed

Lo

gic

H .B .

MUTE G VSW

Thermal

shut-down

OS

C

FGSW

MA

TR

IX

14/180

SANYO DENKI: Fan Motors

15/180

San Ace 120 3-Phase Brushless DC Fan Motor

Sanyo Denki Co., Ltd. is pleased to announce the development of the new 120mm square, 38mm thick "San Ace 120"SG type DC cooling fan motor. This product, slated for release on March 1, 2005, is a high-efficiency DC cooling fan motor ideal for use in personal computers, server and network storage systems, communication instruments, and general-purpose industrial equipment. The San Ace 120 SG type cooling DC has achieved the lowest noise level and one of the highest airflow/static pressures in the industry.

16/180

Motor Drives for Home Appliances

Refrigerators (Compressor Motor)Cooler (Compressor Motor)Washing Machine (Spindle Motor)Dust Cleaning MachineAir Cleaning MachineJuice Machine

17/180

Motor Drive ICs Inside the Intelligent Electronic Toys

i-CybieAibo-2004

18/180

Motor Drive ICs Inside the Intelligent Home Appliances

Crubo (VC-RP30W)Samsung Robot Vacuum CleanerRoomba

4




19/180

Motors in Automobiles

Insight, HONDA, 2000

20/180

Segway to the Future

July 15, 2005 (中國時報) Aug. 12, 2005 (攝於美國佛羅里達 Fort Myers Beach)

21/180

Motor Drives for Manufacturing Automation

Palletizer Application

Winder Application

Cutter Application Blender Application

Catcher/Stacker Application

22/180

Architecture of Motion Control and Motor Drive




23/180

An Example: Motor Drive for Motion Control

+

−

xs Δ x

x*i

indirect position control

+

−

vs

v*i

M

Feed force Fv PartFeed rate vi

direct position control

Table

servomotor

Speedandcurrentcontroller

Positioncontrol

TTacho

positionfeedback

unit

Xi indirectxdirect

E

encoder

24/180

Composition of a Motion Control System

tacho-generator

encoder

servo driveposition controller

control box

5




25/180

Integration of Power, Motor, and Motion Control

Motor

III

III IVtorque

speed

Power Converter

amperes

volts

RBSOA/FBSOA

Four-QuadrantVoltage/AmpereControl

Four-QuadrantTorque/SpeedControl

Closed-LoopSpeed/PositionControl

DSP-BasedDigital Controller

mP/DSP-Based Programmable Motion & Motor Control Techniques

Mechanical Load

X

Y

CoordinatedMotion ProfileControl

New Solutions of Motion Control Problems Using Advanced Technology!

feed drivespindle driveelectrical carelectrical railway.. .. ..

26/180

Control of Motor Drives

Multiple Loop Control Structure of a Positioning Electrical Servo Drive

*fT*fV

*1X

*nX

POSITION

VELOCITY

TORQUE

Pos Ve1 TM

X1 V1 ε1

PWMAmplifier

ServoMotor

LOADCurrent

LoopController

+

_

VelocityLoop

Controller

+

_

PositionLoop

Controller

+

_Motion

Controller

Current FeedbackVelocity Feedback

Position Feedback

27/180

Control Loops and Interfaces: Between Drive and Motion Control Units

PWMAmplifier

ServoMotor

LOADCurrentLoop

Controller

+VelocityLoop

Controller

+_

PositionLoop

Controller

+

_Motion

Controller

Current Feedback

Velocity FeedbackPosition Feedback

TorqueLoop

Controller

Torqueestimator

+

_

PWMControl

Sensorsand

Signal Conditioning Unit

PWM for Power Switches ControlCurrent cmd.Torque cmd.Velocity cmd.Velocity cmd.

Power Conversion ControlTorque (Current) ControlServo (Velocity, Position) ControlMotion (Interpolation, Ramping) Control

28/180

Motor Drive Controllers




29/180

Omnirel: 25 Amp BLDC Motor Driver Module

Applications:• Fans and Pumps• Hoists• Actuator SystemsFeatures:• Fully integrated 3-Phase Brushless DC Motor Control Subsystem

includes power stage, non-isolated driver stage, and controller stage• MOSFET Output Stage• 25A Average Phase Current with 80V Maximum Bus Voltage• Internal Precision Current Sense Resistor (6W max. dissipation)• Speed and Direction Control of Motor• Brake Input for Dynamic Braking of Motor• Overvoltage/Coast Input for Shutdown of All Power Switches• Soft Start for Safe Motor Starting• Unique Hermetic or Plastic Ring Frame Power Flatpacks• Hermetic Package (3.10" x 2.10" x 0.385") F

unct

iona

l Det

ails

of t

he O

M73

93

6




31/180

Application Circuit Schematics Using the OM7393

32/180

IGBT Module for Motor Drive Applications

Motor Controller (μP, DSP, or Control IC)

Voltagedivider

Temperatureamplifier

Currentamplifier gate drive

Powersupply+18 V+5 V

+5 V isolated

+5 V (iso)+5 V+5 V, +18 V

+ +

Three-phaseac input

Three-phaseac input

Drive/controlsection

Powerprintedcircuitboard

Integrated PowerStage (IPS)

Capacitors

Precharge Relay

33/180

Integrated Power Conversion Components

ActiveGate drive AGD AGD

ActiveGate drive AGD AGD

34/180

Development of Integrated Motor Drives

Discrete Input

Discrete Output

Analog Input

RS232C

Man Machine Interface

IR1110 Soft Start

IC

Discrete I/O’s

Analog I/O’s

Serial Comm

AC Drive Motion Profile Processing

Micro controller or

DSP

High Speed Serial Communication

OPTOs

uP/DSP PWM

AD/DA DIO

IR2137 IR2237 Gate

Drive and Protection

IR2171 IR2271

CURRENT FDBKIC

5V.15V

Power Supply

Power Conversio

n Processor

AC MOTOR

45V.15V

600V and 1200V Gate Driver

Switching Power Supply Controller

SPI Communication and Isolator

600V and 1200V Current Sensor

Soft Start Converter Controller

CPU/DSP, I/O, PWM, ADC

35/180

PIIPM50P12B004: Programmable Isolated IPMfrom International Rectifier

PIIPM5012B004: EconoPack 2 outline compatible

FEATURES:DSP (TMS320LF2406A) EmbeddedNPT IGBTs 50A, 1200V10us Short Circuit capabilitySquare RBSOALow Vce(on) (2.15Vtyp @50A, 25 °C)Positive Vce(on) temperature coefficientGen III HexFred TechnologyLow diode VF (1.78Vtyp @50A, 25 °C)Soft reverse recovery2mΩ sensing resistors on all phase outputs and DCbus minus railT/C < 50ppm/°C

Embedded flyback SMPS for floating stages (single 15Vdc @ 300mA input required)

TMS320LF2406A

40MIPS

DC Link Input

Power Module

Current sensecircuit

IR 2213 based gate driver

Encoder/Hall interface

JTAG interface

PI-IPM50P12B004

RS

422

inte

rface

AC/DC motor

36/180

DSP-Controlled Brushless DC Motor

Ref: David C Tam, “DSP-Based Brushless DC Motor Controller," International Rectifier, 1999.

7




37/180

Energy Saving High Power Quality BLDCM Drive

Variable Output PFC Converter + PAM Inverter

85-260 VAC50/60 Hz

VariableOutput

PFCConverter

20 kHz

10-400 VDC(PFC: 50-400V) PAM Inverter

Cd

110 V50/60Hz

dcV

PWM Inverter

BLDC Motor

150 VDC

BLDC Motor

38/180

PFC-Controlled PAM/PWM Multi-Mode BLDC Motor Drive

Co

110/220V50/60Hz

dcV

PWM Inverter

PMSM

Buck-Boost Converter

Lf

uε

ud • PWM Control• Inverter Control• Vector Control• Servo Control

• Power Factor Control

• DC-Link Regulation

HallSensors

Con

trol I

/O

Encoder

Ethernet/I2C NETWORKinterface

I2C

39/180

Integral Motor

風扇框架

控制介面散熱風扇功率驅動與控制模組

行星散熱鰭直流鏈電容

密閉自然散熱變頻馬達電容框架

接線盒40/180

Development of Integral Motor

電控馬達生產廠商

公司名稱產品名稱容量

ABB Integral Motor 0.75-7.5Animate Smart Motor 0.15-7.5Baldor Integral Motor 0.75-7.5Danfoss Integral Motor 0.75-7.5Siemens Integral Motor 0.75-7.5

Alldales Drive Systems Ltd.Little Cross, Church Street, Warnham, West Sussex, RH12 3QS, United Kingdomemail: [email protected]: (01403) 218787Fax: (01403) 218833

41/180

Integrated Vector Drive Servo System

42/180

IP Addressible Electronics-Controlled Integral Motor

CONTROL

COMMUNICATION POWER CONVERSION

MOTOR DESIGN

SYSTEM INTEGRATION

IPEM

Currents

Control

++

ω & θ i

Est LPF

HFP

μ - Processor

IPEM

Con

trol

SYSTEM DESIGNPOWER ELECTRONICSCONTROL FIRM/SOFTWAREDIGITAL IC DESIGNANALOG IC DESIGN

POWER IC DESIGN

EMBEDDED SOFTWARE

DIGITAL SIGNAL PROCESSING

ANALOG SIGNAL PROCESSING

POWER PROCESSING

8




43/180

2005年全球小電機總產量將超過80億台2003年09月29日產經網中國電子報

微小馬達(

9




49/180

Fundamentals of Electric Machinery

Electrical Energy Conversion and Electrical DrivesBasic Physical Laws in Motor ControlElectromechanical Energy ConversionMechanical Interaction Between Motor and LoadStability Analysis of Motor-Load Static OperationMultiple Quadrant OperationMotor BrakingMoment of Inertia

50/180

Electrical Energy Conversion and Electrical Drives

Advantages of Electrical Energy Conversion Process:generated from primary energy (chemical energy in fossil fuel, potential hydro energy, nuclear energy) in relatively efficient central generating stations,transported with low losses over long distances and distributed simply and at acceptable cost,converted into any final form at the point of destination.

Primary Energy

Power Station

Transmission Distribution

Power Electronics

Final Energy Use

Fossil

Nuclear

Solar

Thermal Mechanical Electrical Electrical Mechanical

Controlled Electrical Drives

f0, U0 = const f1, U1 = variableHydro, Wind

Solar (PV)

MechanicalElectricalThermalChemical

Electrical energy per capita and

year 0.1-25 MWh

51/180

Control of Electrical Drives

Due to the progress of automation and with a view to energy conservation, the need for control of electrical drives is likely to become more important in future.

52/180

Architecture of Motor Drive

Controller

PowerAmp Motor

Load

-50

0

50

phase response

10 0 101 102 103 104 10 5

frequency(rad/sec)

100

101

102

103

104

105

101

102

103

magnitude response

frequency(rad/sec)Man-Machine Interface Control Loop Design

PowerSource

53/180

Power Conversion Process

Input Power Power Conversion Output Power

Passive Power ComponentsControl and Sensing Devices

Active Power Devices

battery

mains

Photo

voltaic

DCAC

54/180

Basic PWM Converter Topologies for Motor Drives

Single-Ended Half-Bridge Full-Bridge

Three-Phase Multi-Phase Multi-Level

10




55/180

Matrix Converter as a Power Processor

(a) matrix converter (b) voltage source

Power Processor

InputsOutputs

Utility source

Voltage source

. . .

.

.

.

56/180

Matrix Converter Motor (MCM)

SMPS

IM3~

Auxiliary circuit supply unit(gate-drivers, transducers, control)

ab

c

A B C

Clamp circuit

Inpu

t filt

er

line

C

motor

Mat

rix C

onve

rter

Pow

er S

tage

57/180

Block Diagram of a PM DC Servo Motor Drive

dcV

T1

T2

T3

T4−

+

va

電流控制速度控制位置控制位置命令

全橋式脈寬調變電壓放大器

光電編碼器

直流伺服馬達

T 1 T 2 T 3 T 4

功率晶體

驅動電路

脈寬調變

~

開關式

電源供應器

速度估測

解碼器

濾波器

58/180

Block Diagram of a Practical BLDC Position Servo Drive

dcV

T5

T6

電流控制

&

換相控制

速度控制位置控制位置命令

三相橋式脈寬調變電壓放大器

光電編碼器

無刷直流伺服馬達

T 1 T 2 T 3 T 4

功率晶體

驅動電路

脈寬調變

~

開關式

電源供應器

速度估測

解碼器

濾波器

T3

T4

T1

T2

T 5 T 6

濾波器

59/180


dcV

T5

T6

電流控制

&

換相控制



光電編碼器


T 1 T 2 T 3 T 4

功率晶體

驅動電路

脈寬調變

~

開關式

電源供應器

速度估測

解碼器

濾波器

T3

T4

T1

T2

T 5 T 6

濾波器

60/180

Features of Electrical Drives

Electric drives are available for any power, from 10-6 W in electronic watches to > 108 W for driving pumps in hydro storage plants.They cover a wide range of torque and speed, > 107 Nm, for an ore mill motor, > 105 RPM, for a centrifuge drive.Electric drives are adaptable to almost any operating conditions.Electric drives are operable at a moment's notice and can be fully loaded immediately.Electrical drives are easily controllable.Electrical drives can be designed to operate indefinitely in all four quadrants of the torque-speed-plane without requiring a special reversing gear.Qiet operation and long operating lifeElectrical motors are built in a variety of designs to make them compatible with the load. In special cases, such as machine-tools or the propulsion of tracked vehicles, linear electric drives are also available.

11




61/180

Basic Physical Laws in Motor Control




62/180

Basic Physical Laws in Motor Control

Newton,s Law of Rotation (Rotor Inertia) Torque, Work, and PowerMotion Profile of a Motor Drive Control System Ampere,s LawFaraday,s LawLenz, LawProduction of Induced Force on a WireInduced Voltage on a Conductor Moving in a Magnetic FieldElectromagnetic Energy Conversion

63/180

Newton’s Law

(b) velocity

(c) acceleration

(a) position

64/180

Newton’s Law for Linear Motion

dtdMv

dtdvMMv

dtdff LM +==− )(

fM(t): driving force of the motor in the direction of the velocity vfL(t): load force opposing the motion

M: massv: velocitys: position

M·v: mechanical momentum

Notes:Usually the forces are dependent on velocity v and position s, such as gravitational or frictional forces. The change of mechanical momentum needs a change of force.The motion object is considered as a lumped mass.

Linear Motion

M

vs

fM fL

65/180

Motion with Constant Mass

dtdvMff LM 0=−

Madt

sdMff LM ==− 22

0

2

2

dtsd

dtdva ==

dtdMv

dtdvMMv

dtdff LM +==− )(

If the mass is constant, M = M0 = constant,

0

dtdsv =

where

M

vs

fM fL

66/180

Torque, Work, and Power

θ

T

Torque ( )

Applying a force F to a lever withradius r will produce a torque of

at the pivot point.

N m⋅

F r⋅

T F rF r F r F r

= ⋅=

Σ ( )1 11 1 2 2 3 3- -

Power (Watt)

Power is defined as work done in a given time.

P Wt

Tt

T= = ⋅ = ⋅θ ω [Watt ; Nm, rad / sec]

Work (Joule)

Work is defined as a torque actingthrough a given angulardisplacement.

W T= ⋅ θ [Joule ; Nm , rad ]

radius (r)

force (F)pivot point

F3

r3

F1

r2

F2

r1

T F r= ⋅ [N m ; N, m]

12




67/180

Rotational Motion of Lumped Masses

( )dtdJ

dtdJJ

dtd

LM ωωωττ +==−

Rotational Motion

τM(t): driving torque of the motor in the direction of the angular velocity ωτL(t): load torque opposing the motion

J: inertiaω: angular velocityε: angular position

Jω: mechanical momentum

Notes:It should be noted that τM is the internal or electrical motor torque, not identical with the torque available at the motor shaft. The difference between internal torque and shaft torque is the torque required for accelerating the inertia of the motor itself and overcoming the internal friction torque of the motor.

J

ω, τM

τLε

68/180

Rotation with Constant Inertia

If the inertia is constant, J = J 0 = constant,

0

( )dtdJ

dtd

JJdtd

LM ωω

ωττ +==−dtd

JoLMω

ττ =−

αεττ JdtdJoLM ==− 2

2

2

2

dtd

dtda εω ==

where

dtdεω =

J

ω, τM

τLε

69/180

Moment of Inertia

dtddMr

dtdvdMrdfrd aa

ωτ 2===

A rigid body of arbitrary shape, having the mass M, rotates freely about a vertical axis oriented in the direction of gravity. An element of the mass dM is accelerated in tangential direction by the force element dfa, which corresponds to an element dτa of the accelerating torque

The total accelerating torque follows by integration

ω

dfa

dM

MVr

dτa

dMdtdrd

M

aa

a ωτττ

∫∫ ==0

2

0

70/180

Moment of Inertia of a Rigid Body

dtdJdMr

dtd M

aωωτ == ∫

0

2dMdtdrd

M

aa

a ωτττ

∫∫ ==0

2

0

In the assumption of a rigid body, all its mass elements move with the same angular velocity. The moment of inertia, referred to the axis of rotation, is defined as:

ω

dfa

dM

MVr

dτa

]m[kg 20

2 ⋅= ∫ dMrJM

71/180

Moment of Inertia of Concentric Cylinder

drlrdVdM πσσ 2==

( )414230

2

22

2

1

rrldrrldMrJr

r

M

−=== ∫∫ σππσ

r1, r2 : inner and outer radius of the hollow homogeneous cylinderτL(t): load torque opposing the motion

l: lengthρ: mass densityV: volume of the cylinderJ: moment of inertia

r1

r2ρ

72/180

Inertia of a Solid Rotor

stator

rotor

rotor

Most motors have an inner rotor structure. If the rotor has a radius of 3cm and length of 6cm and it is made of aluminum (ρ=2.7 g/cm3), what is its moment of inertia? [Note: the density of iron is 7.9 g/cm3]

]cm[kg 0.2]cm[g 2.20610.30.67.222

2244 ⋅≈⋅=××==π

σπ

lrJ r

The calculated rotor inertia is about 2.0 kg·cm2, which is the inertia of a 0.5HP induction motor. The rotor inertia of a PM ac servo motor is about 10-30 % of an induction motor with same rating. Low rotor inertia is desirable for servo motors for have a higher acceleration rate.

stator

rotor

13




73/180

Inertia of a Cylinder with a Weight of G

( )2122 rrlgG −= πσ

( )222121 rrri +=

22

12

2

2 ir

gGrr

gGJ =+=

weight G ri : radius of gyrationg : gravitational accelerationρ : mass densityJ : moment of inertia

( )414230

2

22

2

1

rrldrrldMrJr

r

M

−=== ∫∫ σππσ

Notes:The moment of inertia increases with the 4th power of the outer radius. The moment of inertia of a cylinder is proportion to its weight and increases with the square of its radius of gyration.In applications of rotor with low inertia, the rotor has a shape of long cylinder with small radius.

r1

r2ρ

l

74/180

Moment of Inertia of a Rod, Pivoted Out of Center

⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎠⎞

⎜⎝⎛ −+=⎥

⎦

⎤⎢⎣

⎡+== ∫∫∫

− 22

0

2

0

2

0

2 213112 l

aMldrrdrrl

MdMrJalaM

In the above figure, a homogeneous thin rod of length l and mass M is pivoted around a point P, the distance of which from one end of the rod is a.With the mass element dM = (M/l) dr, we can derive the moment of inertia as

The inertia can be expressed as a function of a and we can find the minimum inertia is obtained when the rod is pivoted at the center.

(a) (b)

J

0 1

3

2Ml

12

2Ml

21

la

a

P

M

L-a

75/180

Linking Linear and Rotational Motion

ωττ rvfrfr LLMM === and,

( )dtdrMMv

dtdrLM

ωττ 2==−

2rMJe =

Je : equivalent moment of inertia of the linearly moving mass

M

fMfL

v

τM , ω

τL r

76/180

Effect of Gearing

Why Gearing?Slow motion and high torque is required, such as traction, positioning robots, machine tools, etc.Maximum motor torque is limited by iron saturation (flux saturation) and heat (conductor losses). To increase the motor power density, a simple way is running the motor at high speed and then transfer to the required torque by a gear box.

Effect of gearing on inertia.

To simplify the analysis, we first assume the gear is idea, where two wheels are engaged at the point P with friction, backlash or slip. Assume the left wheel is the driving wheel,

dtd

JfrM 11111ω

τ =−

dtdJfr 2222

ω=

where f1 is the circumferential contact force exerted by wheel 2. Correspondingly, for wheel2 we have:

2ω

2J

2f

1f

1J

1r2r

P

V

11, Mτω

77/180

Gear as a Mechanical Transformer

dtdJfrM 11111ωτ =−

dtdJfr 2222

ω=

221121 , ωω rrff ==

dtdJ

dtdJ

rrJ

dtdJ

rr

dtdJ eM 1112

2

2

11

22

2

1111

ωωωωτ =⎥⎥⎦

⎤

⎢⎢⎣

⎡⎟⎟⎠

⎞⎜⎜⎝

⎛+=+=

Torque of wheel 1 Torque of wheel 2

Balance in force and velocity at the contact point:

2

2

2

112

2

1

211 JN

NJJJJ e ⎟⎟⎠

⎞⎜⎜⎝

⎛+=⎟⎟

⎠

⎞⎜⎜⎝

⎛+=

ωω

where N1 and N2 are the numbers of gears of wheel 1 and 2, respectively.

2ω

2J

2f

1f

1J1r

2r

P

V

11, Mτω

78/180

Multiple Gear of a Hoist Drive

Hoist drive with gear.

[ ]23332

1

32

2

1

211 rMJJJJ e +⎟⎟

⎠

⎞⎜⎜⎝

⎛+⎟⎟

⎠

⎞⎜⎜⎝

⎛+=

ωω

ωω

331

3111 Mgrdt

dJ eM ωωωτ +=

This effective inertia includes the equivalent inertia of the mass M3 being moved in vertical direction. Applying Newtons’s law and taking the load of the hoist into account, we can obtain:

τM1 is the required motor torque for this geared hoist drive.

MOTOR

LossFreegear

11, Mτω

1J 2ω

2J

3ω 3J

3M

32r

This example scows a multiple gear for a hoist drive, where J1, J2, and J3 are the moments of inertia of the different shafts. The total effective inertia referred to shaft 1 is:

14




79/180

Experimental Determination of Inertia

rotor

squirrel-cage induction motor

The moment of inertia of a complex inhomogeneous body, such as the rotor of an electrical machine, containing iron, copper and insulating material with complicated shapes can in practice only be determined by approximation.The problem is even more difficult with mechanical loads, the constructional details of which are usually unknown to the user. Sometimes the moment of inertia is not constant but changes periodically about a mean value, as in the case of a piston compressor with crankshaft and connecting rods.

2

41 MDJ =

D

M is the mass of the cylinder rotor, it can be measured by its weight divided by the gravitational acceleration 9.8m/sec2.

Estimation of the Rotor Inertia

80/180

Run-out Test for Inertia Measurement

The RUN-OUT TEST involves two major steps: Measurement of the steady-state load torque-speed curve. Measurement of the velocity (time) response of the load when the drive power is switched off at an initial constant speed.

ω

t'Lτ)( 1

' ωτ L

1ω

)(tωSteady-state load curve

)(' ωτ L

Coasting curve0ω

1ω

ωdtd

81/180

Torque-Speed Curve Measurement

dtdJpp LM

ωω+=

扭力計(torque meter) 慣性負載馬達 '

Lm

ω

The motor connected load is running at a constant speed by a drive as shown in the above figure. When rotating at constant speed,

0

Now, the input power pM corresponds to the losses of the load, pM = pL. The load power which corresponds to the mechanical power should subtract those loss components, such as armature copper losses. The developed load torque can also be measured by a torque meter connected in the motor shaft.

82/180

Steady-State Torque Estimation

ωωτ lossML

pp −=)('

: load torque at ωω : motor angular velocity

pM : power supplying to the motorploss : power losses in the motor

)(' ωτ L

'Lτ

ω1ω

)( 1' ωτ L

Notes:The motor losses consists of copper losses (I2R), core losses, and windage losses. The copper losses play a dominant factor in these losses and it takes about 85% in the motor losses. If the winding resistance of the motor is known, the copper losses can be calculated from the measurement of the RMS current of the motor windings.

83/180

Run-Out Measurement

ω

t

0ω

扭力計(torque meter) 慣性負載馬達

Measurement Procedure:1. Keep the motor running at a constant speed of ω0. 2. Suddenly turn off the drive power so that the motor-load set is decelerated by the loss torque with

the speed measured as a function of time ω (t).3. The inertia can be calculated from the negative ratio of the load torque and deceleration at a

specified angular velocity.

dtdJLM

ωττ =−

The motor torque τM is turned-off at t=0,

dtd

JLω

τ =−

1

'

ωω

ωτ

=

−≈

dtdJ

L

84/180

Calculation of the Inertia

ω

t'Lτ)( 1

' ωτL

1ω

)(tω

1ω

ωdtd

Steady-state load curve

)(' ωτ L

Coasting curve0ω

1

'

ωω

ωτ

=

−≈

dtdJ

L

1. Give a specified velocity

2. Measure its corresponding load torque

3. Calculate the deceleration rate at the specified velocity.

4. Calculate the estimated inertia

Notes:Graphical constructions, particularly when a differentiation is involved, are only of moderate accuracy. Therefore the inertia should be computed at different speeds in order to form an average.The accuracy requirements regarding inertia are modest; when designing a drive control system, an error of ±10% is usually acceptable without any serious effect.

15




85/180

Special Cases for Initial Measurement

(a) Assuming the corrected loss torque to be approximately constant in a limited speed interval,

then ω(t) resembles a straight line; the inertia is determined from the slope of this line.(a) If a section of the loss torque may be approximated by a straight line,

a linear differential equation results,

The solution is, with ω(t2) = ω2,

Two special cases lead to particularly simple interpretations:

21' for const, ωωωτ

16




91/180

Motion Profile of a Motor Drive Control System




92/180

Motion Profile of a Motor Drive Control System

(c)

(a)

(b)

t

t

t

s1

s1)( sa )( sω )( sθ

a(t) : angular acceleration ω(t) : angular velocityθ(t) : angular positionωm(t)

θm(t)

am (t)

93/180

Motion Profile

t

ωm(t)

The motion profile (speed-time response) of a motor can be used to define as the motion requirement of a specific application.

t

θm(t)

94/180

Maximum Acceleration and Maximum Speed

t

ωm(t)

am(max)(t)

ωm(max)(t)

Maximum SpeedMaximum AccelerationMaximum Deceleration

A motion control system is usually limited by its:

95/180

The Motor Needs a Torque to Accelerate

t

ωm(t)

The differential equation used for the description of the mechanical motion is:

Motor Developed Electrical Torque

eT

Viscous friction torque

Disturbance torque

Load torque

Available torque for acceleration

dtdJTTBTT mmLdmmfeωω ++++= Motor static friction torque

96/180

Motor and Load Dynamics

dtdJTTBTT mmLdmmfeωω ++++=

_mωmT

dT

eT

LJ1

mB

−

LB

−

Load ModelingDisturbance

Modeling

s1

mJ1

s1 mθ

Friction Modeling

)( , mmTF θω

fT LT

17




97/180

The Control Issues

s1

s1)( sa )(sω )(sθ

pK+

−

The proportional control of an double integrator plant is inherently unstable!

acceleration velocity position

The motion of a mechanical system is resulted from an acceleration, constant speed, and deceleration process. If the system is under very small damping (friction), it is inherent unstable!

98/180

Hierarchical Control Architecture of Motor Drive Control

POSITION

VELOCITY

TORQUE

TorqueController

MVelocityController

PositionController

Torquecommand

Velocitycommand

Positioncommand

FeedbackProcessor

Power Conversion (Current & PWM) ControlTorque (Field-Oriented and Commutation) ControlServo (Position & Velocity) ControlMotion (Interpolation & Ramping (Acc./Dec)) Control

99/180

Motor Output Mechanical Power

Controller

PowerAmp Motor

LoadPowerSource

rad/sec]Nm, ;[Watt mmmmm TtT

tWP ωθ ⋅=⋅==

Watts 746HP 1 ==mP (rad/s) 104.7 6021000 RPM 1000 ≈×= π

mP

cmKgw 1m/secKg 1Nm 1 2 ⋅≈⋅=

Nm 0.1Nm 098.0Kgm/sec 098.0m01.09.8m/secKg 1cm Kgw 1 22 ≈==××=⋅100/180

Constant Power and Torque-Speed Operation Area

ωm

T

1mP

2mP

ωm(max)

Tm(max)

101/180

Maximum Power Rate

Power Rate =TP

ΔΔ

(b)

(a)

(a)

t

t

t

ωm(t)

Pm(t)

τm (t)The maximum power rate determines the minimum time for a motor drive system for a given step change of output power.

ωm

T

1mPωm(max)

Tm(max) 102/180

Torque and Back EMF




18




103/180

Basic Relations of Electrical and Magnetic Field

Faraday’s Law

Ampere’s Law

terminalcharacteristics

Corecharacteristics

( )tv ( ) ( )ttB Φ,

( ) ( )tFtH ,( )ti

Magnetic CircuitsElectrical Circuits104/180

Magnetic Field

Magnetic fields are produced by electric currents, which can be macroscopic currents in wires, or microscopic currents associated with electrons in atomic orbits. The magnetic field B is defined in terms of force on moving charge in the Lorentz force law. The interaction of magnetic field with charge leads to many practical applications. Magnetic field sources are essentially dipolar in nature, having a north and south magnetic pole. The SI unit for magnetic field is the Tesla, which can be seen from the magnetic part of the Lorentz force law Fmagnetic = qvB to be composed of (Newton x second)/(Coulomb x meter). A smaller magnetic field unit is the Gauss (1 Tesla = 10,000 Gauss).

105/180

Right-Handed System and Left-Handed System

x

y

z

y

x

z

Right-Handed SystemLeft-Handed System 106/180

Magnetic Field of Current: Right-Handed Rule

The magnetic field lines around a long wire which carries an electric current form concentric circles around the wire. The direction of the magnetic field is perpendicular to the wire and is in the direction the fingers of your right hand would curl if you wrapped them around the wire with your thumb in the direction of the current.

107/180

Ampere’s Law

B H= μ

H = magnetic field intensity (Ampere-turns/m)μ = magnetic permeability of material (Wb/A.m, or Henery/m)B = magnetic flux density (Tesla, Weber/m2)

μ μμr = 0

μ0 = permeability of free space

μ π074 10= × − H / m

μr = relative permeability (between 2000-6000 for general ferromagnetic materials used in electrical machines)

H l I⋅ =∫ dD=10 mm

l=50 mmN=30

WD=1.0 mmWire diameter

I

a

b c

d

∫⎩⎨⎧

=⋅I

Id

enclosenot doescontour if ,0 enclosescontour if ,I

lH

108/180

Permeability

Ampere,s Law H l I⋅ =∫ d

H = magnetic field intensity (Ampere-turns/m)μ = magnetic permeability of material (Wb/A.m, or Henry/m)B = magnetic flux density (Tesla, Weber/m2)

μ μμr = 0

μ0 = permeability of free space

μ π074 10= × − H / m

μr = relative permeability (between 2000-6000 for general ferromagnetic materials used in electrical machines)

perm eability = =μBH

In magnetics, permeability is the ability of a material to conduct flux. The magnitude of the permeability at a given induction is a measure of the ease with which a core material can be magnetized to that induction. It is defined as the ratio of the flux density B to the magnetizing force H. Manufacturers specify permeability in units of Gauss per Oersted (G/Oe).

cgs: = 1 gaussoersted oersted

μ 0410⎡

⎣⎢⎤⎦⎥

= ×tesla mks: = 4 henrry

meterμ π0

710× ⎡⎣⎢

⎤⎦⎥

−

19




109/180

Properties of Ferromagnetic Materials

1.4

1.2

1.0

0.8

0.6

0.4

0.2

00 200 400 600 800 1000

H, A-turn/m

B, Wb/m2

B H= μ μr 0

Ferromagnetic materials, composed of iron and alloys of iron with cobalt, tungsten, nickel, aluminum, and other metals, are by far the most common magnetic materials.Transformers and electric machines are generally designed so that some saturation occurs during normal, rated operating conditions.

DC Excitation

i

N

Φ

110/180

磁通量單位：韋伯 (Wb)

磁通量的國際制(SI)單位，紀念德國物理學家韋伯而命名。簡稱韋﹐用Wb表示。

韋伯定義如下﹕令通過單匝線圈的磁通量在 1秒鐘內均勻地減小到零。如果在該線圈中激發產生的感應電動勢為1伏特，則原來通過該線圈的磁通量為 1韋伯。即1Wb=1V．s。

韋伯是國際單位制的導出單位﹐用基本單位表示的關係式為：

米2‧千克‧秒-2 ‧安培-1 (m 2 ‧kg‧s-2‧A-1)。

1882年西門子在英國科學進展協會上第一次提出以『韋伯』作為磁通量單位，1895年得到英國科學進展協會承認，1948年得到國際計量大會的承認。

韋伯和 CGS電磁系中的磁通量單位馬克斯威之間的換算關係為﹕

1韋伯相當於108馬克斯威。

[1 Wb = 108 Maxwell]

111/180

B-H Curve and Permeability

Relation between B- and H-fields.

H

iB

Bs

HsLinear region

BΔHΔ

HB

ΔΔ

=Δμ

HB

HB

=ΔΔ

=μBΔ

HΔ

HHB r 0μμμ ==

Magnetic intensity H, [A-turns/m]

112/180

Hysteresis Curves of a Ferromagnetic Core in AC Excitation

H

B

Hysteresis Loop

H

B

Br

-Hc

Residual Flux Density

Coercive Force

Magnetization or B-H Curve

area hysteresis loss∝

saturation

113/180

Magnetization Curve of a Ferromagnetic Core

The relationship between B and H for a ferromagnetic material is both nonlinear and multivalued. In general, the characteristics of the material cannot be described analytically. They are commonly presented in graphical form as a set of emperically determined curves based on test samples of the material using methods presented by the American Society for Testing and Materials (ASTM).

(b) AC magnetization B-H curve for M-5 grain-oriented electrical steel 0.03 cm thick (Armco Inc.)

(a) DC magnetization B-H curve for M-5 grain-oriented electrical steel 0.03 cm thick (Armco Inc.)

2.42.22.01.81.61.41.21.00.80.60.40.20

1 10 100 1000 10,000 100,000

B, W

b/m

2

H, A. turns/m

DC Magnetization

H, A. turns/m

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

0

B, W

b/m

2

-10 0 10 20 30 40 50 70 90 110 130 150 170

Scal

e ch

ange

AC Magnetization

114/180

Flux Density or B-Field

Determination of the magnetic field direction via the right-hand in (a) the general case and (b) a specific example of a current-carrying coil wound on a toroidal core.

i

H

(a) (b)

H-field

i

Cross-sectional area A

BA=φ

HHB r 0μμμ ==

20




115/180

Continuity of Flux

A1 A2

A3

φ1 φ2φ3

dABA∫∫=φ 0surface) (closed == ∫∫ dABAφ

∑ =k

k 0φ

0or 0 321332211 =++=++ φφφABABAB

116/180

Magnetic Reluctance and Permeance

Reluctance

Mean path length lCross-sectional

area A

Permeability μ

i

N

Al

μ=ℜ

ℜ=

ℜℑ

=Niφ

∫ ==⋅ NiHld lH

lNiH =

AB

lNiH φμμ ===

ℜℑ=

⎟⎠

⎞⎜⎝

⎛==

Al

Nil

ANi

μ

μφ

Magnetic-motive force (mmf) Ni=ℑ

Permeanceℜ

=Ρ1

117/180

Self Inductance

Amp (I)

Weber-turns (λ=Nφ)

Li

=λ

Mean path length lCross-sectional

area A

Permeability μ

i

N

For a magnetic circuit that has a linear relationship between φ and i because of material of constant permeability or a dominating air gap, we can define the λ-i relationship by the the self-inductance (or inductance) L as

iN

iL φλ == μφ

lANi

= QlAN

lANi

iN

iL μμλ 2===

where λ =Nφ, the flux linkage, is in weber-turns. Inductance is measured in henrys or weber-turns per amp.

118/180

Energy Stored in a Core

Mean path length l Cross-sectional area A

Permeability μ

I

N: number of turns

lANL μ2=

The energy stored in the core:

∫∫ ===tt

L LIdiLiPdtE 02

0 21''

The energy density (energy/volume) is:

μ

μμη

2

211

2

22

222221

B

NlB

lAN

AlAlLI

B

=

⎟⎟⎠

⎞⎜⎜⎝

⎛⎟⎟⎠

⎞⎜⎜⎝

⎛==

The energy stored in the core:

coreBL VLIE η==2

21

Vcore: volume of the core

119/180

Electrical-Magnetic Analogy

Magnetic Circuit Electric Circuitmmf NiFlux φreluctance ℜpermeability μ

viR1/ρ, where ρ=resistivity

+_

Φ

i

N

Φ

ℑ ℜ

120/180

Equivalent Electrical Circuit of a Magnetic Circuit

Reluctance

)H :(unit 1-Al

μ=ℜ

+_

Φ

i

N

Φ

ℑ ℜ

ANi

μφ1

=ℜ=

∑∑ =ℜm

mmk

k iNφ

0=∑k

kφ

ρ/:law sOhm'

AlR

iv

==

∑∑ =m

mk

k vRi :law voltage sKirchhoff'

0 :lawcurrent sKirchhoff' =∑k

ki

Magnetic Electrical

Inductance

ℜ===

2Ni

Ni

L φλ

21




121/180

Magnetic Circuits of a Gapped Core

mean flux path in the ferromagnetic material

N1gAirgap: Hg

i1

l1 = mean path length

Core: H1

i1 in

H

(a) (b)

122/180

Modeling of a Simple Magnetic Circuit

∫ =⋅ IlH dH dl H dl Niia

b

gb

a+ =∫ ∫

Hi : Magnetic field intensity in the ferromagnetic materialHg : Magnetic field intensity in the air gap

magnetic motive force (mmf)(unit: Ampere-turns)

H l H l Nii i g g+ =

mean flux path in theferromagnetic material

v

+

_

li

i

ab

N

lg mean flux path in the air gap

123/180

Modeling of a Simple Magnetic Circuit

B H= μ B lB

l Niii

ig

ggμ μ+ =

Φ = ⋅∫ B SA dFlux

The surface integral of flux density is equal to the flux.

If the flux density is uniformly distributed over the cross-sectional area, then

Φ i i iB A= Φ g g gB A=

The streamlines of the flux density are closed, therefore Φ Φi g=

lA

lA Ni

i

i i

g

g gμ μΦ Φ+ =

ii

ii A

lμ

=ℜgg

gg A

lμ

=ℜ

Nigigi =ℜ+ℜΦ=Φℜ+Φℜ )(

124/180

Modeling of the Air-Gap

gRNi

Φ

v

+

_

li

i

ab

N

lg

mean flux path in the air gap

mean flux path in theferromagnetic material

cR

In general, cg RR >>

125/180

Inductance of a Slot-Cutted Ferrite Core

L NB Ai

N Al

c c c

g

= =2

0μ

v

+

_

i

ab

N

126/180

Control of the Stator Magnetic Field

ωm

r

v

+

_

i

N

)( BLiFvvv

×=

FrT ×=

Stator flux densityRotor winding current

N S

B

BN

S

22




127/180

Faraday’s Law - Change of Flux (Sept. 23, 1831)

Induced voltage from a time-changing magnetic field

Faraday,s Law states that if a flux pass through a turn of a coil of wire, a voltage will be induced in the turn of wire that is directly proportional to the rate of change in the flux with respect to time.

Faraday,s Law

eN

ind voltage induced in the coil = number of turns of wire in coil

= flux passing through coil = N is the flux linkage of the winding

=

φλ φ

e N ddt

ddtind

= − = −φ λ

N turns

φ

inde

128/180

Lenz’ Law - Polarity of Induced Voltage

Lenz, Law

eind

i

direction of i required

dtdNe φ−=ind

The meaning of Lenz,s law:

(1) A coil enclosing an increasing magnetic flux;(2) determining the resulting voltage polarity.

Lenz,s law states that the direction of the voltage buildup in the coil is such

that if the coil ends were short-circuited, it would produce current that would cause a flux opposing the original flux change.

N turns

Direction ofopposing fluxincreasing

+

_

N turns

129/180

Production of Induced Force on a Wire

)( BLiFvvv

×=

Lv

Bv

Fv

θN S

Bv

Lvi

Fv

θsinBLiFvvv

=

A current-carrying conductor in a magnetic field experiences a force acting upon it.

F : force (Newton)B : magnetic flux density (Tesla, Weber/m2)L : length of the conductor (meter)i : current in the conductor (Ampere)

130/180

Production of Induced Force on a Current-Conducting Wire

I

F

BI

N S

B

B

ωm

a

b

c

dvcd r vab

B

I

)( BLiFvvv

×=

rFT ⋅=

131/180

Important Concepts in Electromechanical Motion

In all electromechanical devices, if mechanical motion is occurred, either translational or rotational, this motion will reflect into electric system either as a change of flux linkages in the case of an electromagnetic system or as a change of charge in the case of an electrostatic system.

If the magnetic system is linear, then the change in flux linkages results owing to a change in the inductance.

The inductances of the electric circuits associated with the electromechanical motion devices are functions of the mechanical motion.

132/180

Electromechanical Energy Conversion




23




133/180


CouplingField

MechanicalSystem

ElectricalSystem

Electromechanical systems are comprised of an electrical system, a mechanical system, and a means whereby the electrical and mechanical systems can interact.This interaction can take place through any and all electromagnetic and electrostatic fields which are common to both systems and energy is transferred from one system to the other as a result of this interaction.There are energy losses, energy stored, and energy transferred in the electrical systems, coupling fields, and mechanical systems.

Energy FlowMotor

Generator

134/180


W W W WE e eL eS= + +

W W W WM m mL mS= + +from Energy Conservation Principle: in the coupling field we found

W W W W W W W Ef fL E eL eS M mL mS+ = − − + − −( ) ( )

W W W Wf fL e m+ = +which may also be written as:

Σ ΣΣ

WeL WmLWfL

WM

WmSWf

WmWeWE+

_+ + +

_

__

_ _

WeSElectricalSystem

MechanicalSystem

CouplingField

135/180


The process of converting electrical energy to mechanical energy (or vice versa) isindependent of:(1) the loss of energy in either the electrical or the mechanical systems (WeL and WmL) ,(2) the energies stored in the electric or magnetic fields which are not common to both

systems (WeS),(3) the energies stored in the mechanical system (WmS).

If the losses in the coupling field can be neglected:

W W Wf e m= +

if there is no loss

Σ ΣΣ

WeL WmLWfL

WM

WmSWf

WmWeWE+

_+ + +

_

__

_ _

WeS

WfL=0

136/180

_

Study of an Elementary Electromechanical System

v

+

_e f+i

r L

Φx

x0

M

K

D

ffe

KD

v

r

efL

Φ

applied voltagecurrentresistance of the current-carrying conductorinductance of the electromechanical systemvoltage drop across the coupling fieldflux in the coupling fielddeveloped electromechanical forceexternal mechanical forcemass of the moving weightequilibrium positionposition of the moving massspring constantdamping coefficient

i

x0x

M

Electrical equation of the electrical system;

Mechanical equation of the mechanical system;

v ri L didt ef= + +

f M d xdt

D dxdt K x x fe= + + − −2

2 0( )

ffe

K

D

137/180

Operating Modes and Motor-Load Torque-Speed Characteristics




138/180

Operating Modes of an Electrical Drive

Motor Load

ω, τMτM = Motor torqueτL = Load torque

τL

V (ω)

fM (τM)

Driving

Driving

Braking

Braking

vv

v v

fMfM

fM fM

ωm

T0

I

ωm1 Maximumpower

Maximumtorque

−ωm3

−ωm2

3SIII IV

II

D

C

A

B

F

E

TL

TL

2S

1S

Maximumspeed

24




139/180

馬達與負載之扭矩方程式

Motor Load

TLT

ωm

T T J ddtL

m= +ω

Motor Developed Torque = Load Torque + Dynamic Torque

J = load inertia referred to the motor shaft, Kg - m2

ωm = instantaneous angular velocity of the motor shaft, N - mT = motor developed torque, N - m

TL = load torque referred to the motor shaft, N - m

ωmSpeed

Torque Tm

ωmSpeed

Torque TL

140/180

Compositions of Load Torque

Load Torque TL = Friction Torque TF + Windage Torque TW + Work Torque TM

ωm

Torque

0 Ts

TvTc

TcTv

Ts

ωm

TF0

Friction torque and its components

Friction Torque TF = Viscous Friction Tv + Columb Friction Tc + Static Friction Ts

T T B T CL M m c m= + + +ω ω 2

can be neglected

windage torquecoulomb friction

viscous friction

141/180

Examples of Load Torque Characteristics

ωm

TL

ωm

TL

ωm

T

Pd1Pd2

0

Pd1Pd2

ωm

T

Pd1Pd2

0

Pd3S1S2

A*B*

AB

C*C

ωm

TL0

A

A*

B

B*

C

0TL

ωm lowspeed

highspeed

(a) Fan and centrifugal pumps (b) Traction excluding gravity (c) Coiler drives

(d) Diesel-electric locomotive (e) Excavators (f) Hoist

142/180

Examples of Motor Torque Characteristics

split-series motorstraight-series motor

Speed

Torque

DC servo motor shunt motor compound motor

Induction motor

Speed

Torque

Speed

Torque

Speed

Torque

Speed

Torque

Speed

Torque

143/180

扭矩轉速曲線下的穩態穩定平衡點

( ) ( ) ( ) 0=Δ+−Δ++Δ+ TTTTdt

dJ eLemmωω

( ) 0=Δ−Δ+ TTdt

dJ Lmω

( ) 0=Δ⎥⎦

⎤⎢⎣

⎡−+

Δm

m

Lm

ddT

ddT

dtdJ ω

ωωω

( )t

ddT

ddT

Jomm

mm

L

e⎟⎟⎠

⎞⎜⎜⎝

⎛−−

Δ=Δ ωωωω1

0>−mm

L

ddT

ddT

ωω

Lee TT = 0=dtd mω與

mmd

dTT ωω

Δ⎟⎟⎠

⎞⎜⎜⎝

⎛=Δ m

m

LL d

dTT ωω

Δ⎟⎟⎠

⎞⎜⎜⎝

⎛=Δ與

穩態平衡工作點必須符合之條件

ωm

Torque

A

B

C

Load torque TL1

Motor torque T

Load torque TL2

0

Speed

144/180

多象限扭矩─轉速曲線在不同之轉速設定與負載特性

ωm

T0

III

Maximumpower

Maximumtorque

TL

TL

III IV

Speedsettings

Base speed

Base speed

Maximum speed1

2

3

4

5

6

7

8

9

10

11

12

13

25




145/180

Four-Quadrant Operation & Torque-Speed Trajectories

ωm

T0

I

ωm1 Maximumpower

Maximumtorque

−ωm3

−ωm2

3SIII

IV

II

D

C

A

B

F

E

TL

TL

2S

1S

Maximumspeed

146/180

多象限工作區的速度變化扭矩─轉速曲線圖：(a)減速 (b)反轉 (c)加速

III

ωm

T

ωm1

ωm2

S1

S20

A

B

C

Maximumpower

Maximumtorque

TLωm

T0

III

ωm1 S1A

B

C

Maximumpower

Maximumtorque

TL

−ωm1

−ωm2

F

E

D

TL

2S

3SIII IV

III

ωm

T

ωm1

ωm2

S1

S20

A

B

C

TL

Maximumpower

Maximumtorque

(a)

(b)

(c)

147/180

不同『馬達─負載扭矩轉速曲線』的工作點

ωm

Torque0

B

TL2T

ATL1

ωm

Torque0TL1

CTL2

T

D

ωm

Torque0

TLF

T

E

ωm

Torque0

T

G

TLH

(a) (b)

(c) (d) 148/180

馬達剎車 (Motor Braking)

再生剎車(regenerative braking)

馬達剎車機械式剎車

電氣式剎車動態剎車(dynamic braking)

149/180

馬達與驅動器的多象限操作

Multiple quadrant operation of electrical motors and drives.

reversebraking

torque

forwardmotoring

reversemotoring

forwardbreaking

III

III IV

speed ωm

T0

III

Maximumpower

Maximumtorque

TL

TL

III IV

Speedsettings

Base speed

Base speed

Maximum speed1

2

3

4

5

6

7

8

9

10

11

12

13

150/180

Typical Torque-Speed Operating Curves of Servo Motor

26




151/180

馬達的功率轉換、損失分析與選擇




152/180

Power Flow of DC Generator

I2R losses

P conversion

AAm IE=ωτ indmP ωτ appin =

Core lossesMechanical

lossesStray losses

LTVVP =out

153/180

Power Flow of DC Motor

I2R losses

P conversion

mAAIE ωτ ind=mP ωτ landout =

Core lossesMechanical

losses

Stray losses

LTVVP =in

154/180

Servo Motor Selection: Direct Drive

155/180

Servo Motor Selection: Calculation of Inertia

156/180

Servo Motor Selection: Gear Drive

mT JNJ

J += 21

NeT

Tm 1=

27




157/180

Servo Motor Selection: RMS Torque

Tttt dPeLaP

rms⋅+⋅+⋅

=222 ττττ

啟動行進剎車

時間 (sec)

V Nt M( )

Pτ

Lτ

Pτ

t a t e td

循環週期 T

停止

158/180

Motor Sizing and Selection

Load Torque-Speed Characteristics Cost, Efficiency, Volume, Performance Considerations Motor Type Selection Motor Torque-Speed Operation AreaTypical Motion Profile Calculated RMS TorqueLoss AnalysisTemperature Rise & Winding Insulation ClassMaximum Power Rate

159/180

馬達與驅動器的分類與應用




160/180

馬達之分類

馬達

串激式、並激式、分激式馬達

永磁式直流馬達

直流馬達

交流馬達

步進馬達

其他: 如音圈馬達、超音波馬達、微型馬達等

同步式 (轉子永磁型、轉子電激型)

感應式 (轉子鼠籠型、轉子繞線型)

永磁式

磁阻式

磁阻式 (開關式、同步式)旋轉型

線型

線性直流馬達

線性交流馬達

線性步進馬達

161/180

Classification of AC Motors

AC MOTOR

Sinusoidal-fed Rectangular-fed

Brushless DC SwitchedreluctanceInduction Synchronous

Squirrel-cage

Wound-rotor

Wound-rotor

PMrotor Reluctance

Surface-mounted

Interior-mounted

162/180

伺服馬達之分類

永磁式交流伺服馬達

(無刷式直流伺服馬達，永磁式同步馬達)

感應式交流伺服馬達

伺服馬達

有刷式永磁式直流伺服馬達

無刷式

28




163/180

Motor Construction Possibilities

rotor

stator rotor

stator

rotor

stator

rotor

stator

(a) (b)

(c) (d)164/180

DC Servo Motor

165/180

Structure and Functional Description of a PM DC Motor

Environmentally protected models-Explosion Proof and Wash Down Duty

Permanent magnet fields are more efficient, smaller, lighter and offer wider speed range than comparable wound field motors

Long life, constant force brush springs with field replaceable brushes

Rugged, fused commutator

TEFC and TENV configurations

Conduit box (gasketed) -large wiring compartment for easy termination

NEMA or metric mounting

Large sealed bearings are standard

Class H insulation

Polyester impregnated armature for electrical and mechanical integrity

Patented anti-cog magnets for smooth low speed operation. High overcurrent capacity and dynamic braking without demagetization

166/180

Decomposition of a BLDC Servo Motor

167/180

State of the Art: AC Servos

High Speed Spindle(Siemens)

DSD Servo (Baumüller)High Torque Motor

(Baumüller)Spindle Motor (Franz Kessler)

168/180

Typical Specs. of PM AC Servo Motors

29




169/180

PM AC Servo Motor

S

N

A B C

θ

sin ω et

sin ( )ω πet +23

sin ( )ω πet +43

electroniccommutator

Vm sin θ

Vm sin( )θπ

+23

Vm sin( )θπ

+43

V tm esin( )ω θ+

V tm ecosω V tm esinω

V tm esin( )ω θ+

Three Phase, 2-Pole Motor

Permanent Magnet Rotor

a r

ar'

brb r'

cr

c r'

a s

as'

bs

b s'

c s

cs'

S N

N

S

170/180

AC Induction Motor

aluminum bars for carrying induced current

Squirrel Cage Rotor Lamination(cutaway view)

shaft hole

steel lamination plate

Rotor current induced by stator fieldUses 3-phase power inverter

ar

a r'

br

b r'

cr

cr'

rotor

stator

stator axisrotor axis

a s

as'

bs

b s'

c s

c s'

171/180

Photos of a Squirrel-Cage Induction Motor

(a) squirrel-cage induction motor and (b) its inside structure.

(a) (b)

172/180

Switched Reluctance Motor

steel rotor

Three Phase 6/4 Motor

these coils on now

these coils on next

rotationdirection

Classical SR Drive Converter

motor coils in series with switching devices

♦ rotation produced to minimize the magnetic reluctance (resistance)

173/180

Hybrid Step Motor

MS connector termination for motor and optical encoder. Flying leads and terminal board via conduit termination also standard.

Optional line driver encoders-200 to 1024 PPR.

Rare earth rotor magnets provide high demagnetization resistance.

Sigmax® technology in K series adds flux concentrating rare earth stator magnets for even higher torque and acceleration than N series.

Large diameter rotor coupled with optimum magnetic design produces highest torque and acceleration-both N and K series.

Long life bearings withstand high radial and axial forces.

Straight key. Other options available. Optional shaft sizes and special designs (spline, for example) available.

Rugged, square frame housinglessdesign provides NEMA and IP65 splash proof construction.

Standard NEMA mounting.

174/180

驅動器的種類

直流伺服驅動器

泛用型變頻器

向量控制變頻器

永磁式交流伺服驅動器

感應式交流伺服驅動器

無感測變頻器

無感測向量控制變頻器

泛用型向量控制交流驅動器

30




175/180

Block Diagram of a PM DC Servo Motor Drive

dcV

T1

T2

T3

T4−

+

va

電流控制速度控制位置控制位置命令

全橋式脈寬調變電壓放大器

光電編碼器

直流伺服馬達

T 1 T 2 T 3 T 4

功率晶體

驅動電路

脈寬調變

~

開關式

電源供應器

速度估測

解碼器

濾波器

176/180


dcV

T5

T6

電流控制

&

換相控制



光電編碼器


T 1 T 2 T 3 T 4

功率晶體

驅動電路

脈寬調變

~

開關式

電源供應器

速度估測

解碼器

濾波器

T3

T4

T1

T2

T 5 T 6

濾波器

177/180

交流驅動器的發展趨勢

泛用型交流伺服驅動器

專用型交伺服流驅動器

專用型無感測變頻器

泛用型變頻器

交流驅動器的發展趨勢 Universal Auto-Tuning AC Drive

178/180

Inverters for 3-Phase Motor Drive Applications

Voltage (Line to Neutral)

Current (Line)

179/180

References

[1] DC Motors, Speed Controls, Servo Systems, including Optical Encoders, An Engineering Handbookby Electro-Craft Corporation, Hopkins, MN, Fifth Edition, 1980.

[2] R. Krishnan, Electric Motor Drives: Modeling, Analysis, and Control, Prentice Hall, February 15, 2001.[3] Werner Leonhard, Control of Electrical Drives, 3nd edition, Springer Verlag, January 15, 2001. [4] P. C. Krause, O. Wasynczuk, and S. D. Sudhoff, Analysis of Electric Machinery and Drive Systems,

IEEE Press and Wiley Inter-Science, 2002.

[5] Ned Mohan, Advanced Electric Drives: Analysis, Control and Modeling using Simulink, MNPERE, Oct. 2000.

[6] Ned Mohan, First Course on Power Electronics and Drives, MNPERE, July 15, 2003.[7] D. W. Novotny and T. A. Lipo, Vector Control and Dynamics of AC Drives, Clarendon Pr, USA,

September 1996.

[8] Chee-Mun Ong, Dynamic Simulation of Electric Machinery: Using MATLAB/Simulink, Prentice Hall, 1998.

[9] Edied by: B. K. Bose, Power Electronics and Variable Frequency Drives – Technology and Applications, IEEE Press, 1997.

[10] P. C. Sen, Principles of Electric Machines and Power Electronics, Second Edition, John Wiley & Sons, 1997.

[11] J. Chapman, Electric Machinery Fundamentals, McGraw-Hill, 1991.[12] A. E. Fitzgerald, C.K. Jr., and S.D. Umans, Electric Machinery, McGraw-Hill Book Company, 1983.

180/180

References

[13] Vincent Del Toro, Electromechanical Devices for Energy Conversion and Control Systems, Prentice-Hall, 1976.

[14] G. Rizzoni, Principles and Applications of Electrical Engineering, International Student Edition, Richard Irwin, Inc., 1993; ISBN 0-256-12969-X

[15] A. Hughes, Electric Motors & Drives - fundamentals, types & applications, Heinemann Newnes, 1990, ISBN 0-434-90795-2

[16] T. Kenjo, Electric Motors and their Control, Oxford University Press, 1991 (re-printed: 1993, 1994, 1996, 1998); ISBN 0 19 856240 3

[17] B. C. Kuo and J. Tal, DC Motors and Control Systems, 1978.

電動機控制的理論基礎pemclab.cn.nctu.edu.tw/W3news/技術專欄/2007-05-17...2007/05/17...

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Transcript of 電動機控制的理論基礎pemclab.cn.nctu.edu.tw/W3news/技術專欄/2007-05-17...2007/05/17...